As soon as you find out your flight got cancelled call your airiline because in the case of fog many flights will be impacted and many people will be stranded in London. If you are flying with British Airways call their Reservation Service immediately at 0800 727 800. (The country code for calling a number in the UK is ++44) and book the next possible flight out. If you wait with the booking you might not get anymore a seat on a plane the next day.
For the call you either need the flight number of the cancelled flight or your E-Ticket Number.

Next step secure yourself a hotel room if you have to stay overnight. British Airways will imburse Hotel Accomodation up to 200£ per day per room – 2 people sharing), the transport between the airport and hotel (£50 for the round trip) and a reasonable meal and refreshment expenses (£25 per adult per day and £12.50 for children) and two reasonable phone calls per passenger. You need to spend first and then hand in your receipt with the reason at their
BA Cusotmer Relations (S506)
P.O. Box 5619
Sudbury
Suffolk C0102PG
If you are already at London Heathrow Terminal 5 go to the arrival area outside the security area. There is a hotel reservation desk that will organize a stay for you.

Once you have secured your place in a hotel in London make sure you are back at the London airport early in the morning. I had to get my ticket issued at London Heathrow Terminal 5 and there are only 3 counters at the section with a long queue of people waiting at 7:35 am in the morning. London Heathrow airport will open at 5 am in the morning.

In my case I only had to show my passport to get my ticket. Additionally I got 2 vouchers for £10 each to have a meal at the airport which I currently enjoy.

Hope this information was helpful and I would very much appreciate if you had any additionally advise to share in the case of cancelled flights in England because it would improve the whole situation for you and others if the fog strikes again.

This information was helpful, whenever this happened to anyone it hassles alot, as if someone does not get the right and secure car parking then it hassles. Thus valet parking Gatwick kind of services are amazingly helping.